Collector Droplet Behavior during Formation of Nanowire Junctions.

Formation of nanowire networks is an appealing strategy for demonstrating novel phenomena at the nanoscale, e.g., detection of Majorana Fermions, as well as an essential step in realizing complex nanowire-based architectures. However, a detailed description of mechanisms taking place during growth of such complex structures is lacking. Here, the experimental observations of gold-catalyzed germanium nanowire junction formation are explained utilizing phase field modeling corroborated with real-time in situ scanning electron microscopy. When the two nanowires collide head on during the growth, we observe two scenarios. (i) Two catalytic droplets merge into one, and the growth continues as a single nanowire. (ii) The droplets merge and subsequently split again, giving rise to the growth of two daughter nanowires. Both the experiments and modeling indicate the critical importance of the liquid-solid growth interface anisotropy and the growth kinetics in facilitating the structural transition during the nanowire merging process.

One of the envisioned unique advantages of one-dimensional nanostructures is their potential for three-dimensional stacking, which allows formation of complex architectures 1,2 for future electronics and nanophotonics. Crossed nanowire systems represent an effective platform for detection and manipulation of Majorana fermions, [3][4][5][6] that are intensively investigated for quantum computing considering their robust topological characteristics. [7][8] Also, for designing thermoelectric nanoscale systems, phonon transport engineering in one-dimensional systems provides a promising route, [9][10] where a recent interest has been naturally raised at nanowire junctions, going beyond a single wire architecture. [11][12][13] However, it is still challenging for the realization of precisely engineered networks of nanowire junctions.
Fabrication of nanowire-based devices requires a synthesis approach that results into the nanowire growth at positions predefined by lithography. In this regard, two techniques have become prominent. In catalyst-free approach (also denoted as selective area epitaxy) 14 the nanowires nucleate within openings in an oxide or nitride mask and elongate in one dimension due to an interplay between the surface energies of different facets. The second approach utilizes the vapor-liquid-solid (VLS) mechanism, 15 which allows size-selective nucleation of nanowires from supersaturated catalyst nanoparticles. The nanoparticle size determines the nanowire diameter and, given that the nanoparticles can be placed onto a growth substrate with nanometerscale precision, [16][17][18] VLS growth can achieve control of the nanowire size and location with the accuracy comparable with the catalyst-free approach. In both growth approaches, a nanowire junction can be subsequently formed by the collision of two nanowires growing in crystallographically well-defined growth directions towards each other. The feasibility of this process has been demonstrated by utilizing either planar [19][20][21][22] or patterned [23][24] substrates to create dense arrays of nanowire junctions and even interconnected nanowire heterostructures. 25 4 Despite these achievements, the final junction geometry is difficult to control. In the catalyst-free approach, "X", "V" and "Y" junction shapes have been reported, 5,26-28 among which a frequent observation is the "X" shape as a consequence of misalignment of the colliding nanowires. In this case, the nanowire top facet remains partially accessible to the growth species and, thus, both nanowires proceed in their original growth direction despite the junction formation. On the contrary, in the VLS growth, more complex shapes could be formed, 24,27 which is closely related to the droplet dynamics upon droplet collision event. In general, this collision can be categorized into two types: tip-to-side and tip-to-tip. In the tip-to-side nanowire collisions, it has been demonstrated that the droplet of the colliding nanowire either slides down after hitting the other wire sidewall 20,23 or bounces off (forming a "K" shape junction). 22 In tip-to-tip collisions the droplets have been reported to merge into one during a collision event, 29 which inevitably results in the decrease of nanowire density. This could be prevented by subsequent droplet splitting and formation of "X" junctions. Nevertheless, understanding of the governing mechanisms of junction formation in tip-to-tip collisions remains unexplored yet. Here, we investigate the tip-totip collisions of Au-catalyzed Ge nanowires employing both phase field simulations and real-time in-situ electron microscopy observations. We identify the critical importance of the shape of liquid-solid growth interface and the growth kinetics in determining the droplet behavior and the final junction geometry. Our findings should shed more light onto the very complex junction formation mechanism, and inspire new strategies for optimizing synthesis pathways of nanowire networks.
To study the effect of the growth conditions on the junction formation, and to avoid any possible influence of substrate pre-patterning, we have utilized epi-ready Ge(100) wafers which were processed via a standard protocol before the nanowire growth. Namely, the wafers were cleaned 5 in acetone, IPA and water, followed by immersing into an HF-modified 16 Au colloid solution (nanoparticles with 20 or 80 nm in diameter) to deposit catalyst particles. The samples were immediately loaded into either a high vacuum growth chamber or a modified scanning electron microscope (SEM) equipped with a germanium evaporation cell. Both experimental layouts are  In our experiments, gold-catalyzed germanium nanowire growth is achieved under high vacuum conditions by evaporation from a solid source. This deposition technique is known to result in nanowires growing in the <110> direction, which exhibit a hexagonal cross-section with four {111}-oriented and two {100}-oriented sidewalls. 31, 32 The growth interface is not planar, but 5 in acetone, IPA and water, followed by immersing into an HF-modified 16   In our experiments, gold-catalyzed germanium nanowire growth is achieved under high vacuum conditions by evaporation from a solid source. This deposition technique is known to result in nanowires growing in the <110> direction, which exhibit a hexagonal cross-section with four {111}-oriented and two {100}-oriented sidewalls. 31, 32 The growth interface is not planar, but 5 in acetone, IPA and water, followed by immersing into an HF-modified 16   In our experiments, gold-catalyzed germanium nanowire growth is achieved under high vacuum conditions by evaporation from a solid source. This deposition technique is known to result in nanowires growing in the <110> direction, which exhibit a hexagonal cross-section with four {111}-oriented and two {100}-oriented sidewalls. 31, 32 The growth interface is not planar, but 6 consists of two inclined {111} planes, forming an inverted V-shape. 31 Owing to the crystal symmetry, there exist four equivalently possible out-of-plane <110> growth directions, which enhances the probability of nanowire collisions ( Fig. 1), thus providing a nice playground for studying the junction formation phenomena. Fig. 1a shows the growth conducted at 380 °C, slightly above the gold-germanium eutectic temperature. Under these conditions, "Y" junctions are formed (two nanowires merging into one). The nanowire originating from the collision point is larger in diameter (as the droplet volume increases after merging of the initial ones) and its growth direction is <111> with a rather complicated sidewall morphology. 30 If the growth is conducted at the higher temperature, "X" junctions are occasionally observed (droplet splits into two after merging and they catalyze the growth of two daughter nanowires, see Fig. 1b). Similar to the low-temperature collision event, the resulting nanowires grow into the <111> direction.
The yield of "X" junctions on this sample is around 15%, while on the sample prepared at lower temperature only "Y" junctions were found (slightly more than 100 nanowire junctions were inspected in each case). It should be noted that the geometrical configuration of the nanowires before the junction formation is not decisive onto the particular growth direction after the junction formation -we observe all the possible <111> directions (see Supporting Information, Fig. S1). For further discussion, it is also important to note that the higher growth temperature results into the higher growth rate of nanowires (see Supporting Information, Fig. S2, for growth rate quantification). 31 That is a direct consequence of the growth mechanism, since the growth rate is limited by the surface diffusion of germanium adatoms towards the catalytic droplet. The experiments also revealed that the junction formation is not sensitive to the droplet diameter (within the studied range, 70 -350 nm).  S2) the droplets merge into a single larger one, and the "Y" junction is formed as a result of continuing growth. If the growth rate is increased ( ≈ 8.7 nm/min, Fig. S2) the droplet splits after merging, yielding the "X" junction formation if left developing further (Fig. 2b). It should be noted that under a given condition, there is no variation in the type ("X" or "Y") of the junction structures evolved in simulations (e.g. in the high growth rate case, the model consistently predicts an "X" shape). That is in contrast to experiments, where the yield of "X" junctions is much smaller. This discrepancy comes from the deterministic nature of our current model, where the local environmental and thermal fluctuations in experimental growth systems are not specifically considered.

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The simulation results, together with experimental observations, support the hypothesis that the droplet splitting is an activated process, requiring additional energy to overcome the related kinetic barrier. This is achieved by increasing the growth temperature in experiment or by directly raising the chemical potential driving force in the simulation. These two quantities can be satisfactorily correlated by comparing their effects on the nanowire growth rate (Supporting Information, Fig. S2). Such approach provides a link between experiments and simulations, overcoming the difficulty in directly quantifying the chemical potential driving force from an experiment. 9 The simulation results, together with experimental observations, support the hypothesis that the droplet splitting is an activated process, requiring additional energy to overcome the related kinetic barrier. This is achieved by increasing the growth temperature in experiment or by directly raising the chemical potential driving force in the simulation. These two quantities can be satisfactorily correlated by comparing their effects on the nanowire growth rate (Supporting Information, Fig. S2). Such approach provides a link between experiments and simulations, overcoming the difficulty in directly quantifying the chemical potential driving force from an experiment. 9 The simulation results, together with experimental observations, support the hypothesis that the droplet splitting is an activated process, requiring additional energy to overcome the related kinetic barrier. This is achieved by increasing the growth temperature in experiment or by directly raising the chemical potential driving force in the simulation. These two quantities can be satisfactorily correlated by comparing their effects on the nanowire growth rate (Supporting Information, Fig. S2). Such approach provides a link between experiments and simulations, overcoming the difficulty in directly quantifying the chemical potential driving force from an experiment. Here we further discuss the growth direction change after the collision event. The splitting of the droplet naturally results into formation of two new liquid-solid growth interfaces with the <111>orientation. The two wires growing after the splitting thus grow in <111>-direction, in contrast to the initial <110>. It should be noted that the <111>-oriented nanowires exhibit different morphology compared to those of the <110> direction. But just as the case of the <110>-oriented wires, the simulation predicted morphology 34 reasonably matches the one observed experimentally. 30 Extensive modelling has shown that kinking from <110> to <111> is feasible under the most experimental conditions. There is, however, one exception. Figures S3 and S4 in Supporting Information show the case of perfectly aligned colliding nanowires, again under the conditions of slow and fast growth. The resulting junction shape is not affected by the geometry of the collision (i.e. the angle between the colliding nanowires), however, in case of slow growth the kinking of the resulting nanowire towards <111> does not take place. Despite other effects, e.g. nanowire diameter, 33 these additional simulations we have performed suggest that kinking after collision event may be related to the misalignment of the colliding nanowires. As a consequence of the off-axis collision, the droplet wetting configuration changes to an asymmetric one which results in the subsequent growth direction change ( Fig. 2a and Fig. 3b). A similar kinking phenomenon is captured by applying external force perturbation on the droplet to mimic the droplet oscillation (see Supporting Information, Figure S5, and ref. 35). Additionally, such behavior indicates that the <110> direction could be a metastable growth direction, while the <111> represents a stable state.
Finally, additional simulations reveal that for the occurrence of the splitting process, the dropletnanowire contact geometry is one critical factor in lowering the related kinetic barrier. This finding is verified by our simulations of the evolution of a droplet wetting of two crossed nanowires with flat liquid-solid interfaces (by assigning isotropic interfacial energies in the model, Fig. 4). In this case, despite the higher chemical potential driving force which is anticipated to promote splitting (Fig. 2b), the droplet does not split, and the nanowire junction evolves towards a "Y" shape. This result emphasizes the importance of growth interface anisotropy as a key influential factor in determination of the final nanowire junction shape.
Presumably, the inverse-V shaped liquid-solid interface can facilitate the formation of "X" junctions, by offering a kinetic pathway for droplet splitting with lower activation energy. The splitting does not occur despite the larger growth rate (compare to Fig. 2b, where the growth rate is the same).
The tendency of the droplet to split could also be dependent on other factors that are not inspected here. For example, the surface free energy of the liquid can affect the droplet stability on top of a nanowire. It has been theoretically proposed that the splitting of the droplet may be energetically favorable if catalysts with low surface energy are used for promoting the nanowire growth, 36,37 though such behavior was observed very rarely. 37 The effect of the surface energy of the liquid on droplet stability is size-dependent, which is found to be more profound for very small nanowire diameters. In our experiments, we have not observed noticeable size-effects (our 13 nanowires have diameters of 70-350 nm), but this may not be the case for much smaller droplet diameters. However, to study the size-effects on splitting is beyond the scope of this paper.
The conclusions derived from our simulations can possibly be extended to other material systems, e.g. III-V nanowires which predominantly grow in <111> growth directions with the liquid-solid interface formed by a {111} plane. Depending on the growth conditions, this growth plane may become truncated; the droplet supersaturation determines the extension of this truncation. 35 The truncation facets have been observed experimentally, e.g. for GaAs, 38 GaP, 39 InAs 40 and sapphire; 41 and similarly in computer simulations. 35,42 Based on our predictive results, one could expect that possibly the "X" junctions (resulting from the splitting of a merged droplet) can also be seen in other VLS-grown nanowires with large enough growth plane truncation (i.e., anisotropic liquid-solid interface) under specific growth conditions. In fact, the junction shapes in some of the systems have been reported very recently. 24 In summary, we have shown that the nanowires grown by the vapor-liquid-solid approach can be engineered to form junctions of a desirable shape by carefully tuning the experimental conditions.
The experimental results are corroborated by extensive phase field simulations, which have unravelled the crucial importance of the growth interface anisotropy and the growth kinetics on the resulting junction shape. The droplets on top of merged wires are more prone to splitting if the liquid-solid interface evolves towards an anisotropic shape, which is inherent to some catalyst/nanowire systems (in the case of Au-catalyzed Ge nanowires, as shown here, the growth interface is V-shaped along the <110> orientation) or can be experimentally controlled by altering the growth conditions (in the case of III-V nanowires, large droplet supersaturation results in significant truncation of the top nanowire facet beneath the droplet). Our findings are thus not limited within the material system studied in this paper but should be more generally applicable to other nanowire systems, as useful guidelines for designing and tailoring junction geometries.

Experimental Methods
Phase Field Simulations. A 3D multi-phase field model, 34 (temperature/current passing the heating element) was validated in a separate experiment in SEM using temperature-indicating suspensions. The evaporation rate was controlled by changing the evaporator crucible temperature and was calibrated before the experiment using a crystal quartz thickness monitor. The incidence angle of germanium atoms on the sample with respect to the sample normal was 70°. In the case of real-time SEM experiments, the evaporation geometry was the same, and the electron beam was incident under 52° to the sample normal.